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Fredholmness and invertibility of Toeplitz operators with matrix almost periodic symbols
Authors:
Leiba Rodman, Ilya M. Spitkovsky and Hugo J. Woerdeman
Journal:
Proc. Amer. Math. Soc. 130 (2002), 1365-1370
MSC (2000):
Primary 47B35, 43A60
Posted:
September 19, 2001
MathSciNet review:
1879958
Full-text PDF Free Access
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Abstract: We consider Toeplitz operators with symbols that are almost periodic matrix functions of several variables. It is shown that under certain conditions on the group generated by the Fourier support of the symbol, a Toeplitz operator is Fredholm if and only if it is invertible.
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- A. Böttcher, Yu. I. Karlovich, and V. S. Rabinovich.
The method of limit operators for one-dimensional singular integrals with slowly oscillating data.
J. Operator Theory, 43:171-198, 2000. MR 2001d:45004
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- A. Böttcher, Yu. I. Karlovich, and I. M. Spitkovsky.
Convolution Operators and Factorization of Almost Periodic Matrix Functions.
In preparation.
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- L. Coburn, R. D. Moyer, and I. M. Singer.
 -algebras of almost periodic pseudo-differential operators.
Acta Math., 130:279-307, 1973. MR 54:3495
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- C. Corduneanu.
Almost Periodic Functions.
J. Wiley & Sons, 1968. MR 58:2006
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- Yu. I. Karlovich.
Algebras of convolution type operators with discrete groups of shifts and oscillating coefficients.
Doctoral dissertation, Mathematical Institute, Georgian Academy of Sciences, Tbilisi, 1991.
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- Yu. I. Karlovich.
On the Haseman problem.
Demonstratio Math., 26:581-595, 1993. MR 95a:47048
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(Semi)-Fredholmness of convolution operators on the spaces of Bessel potentials.
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Linear Topological Spaces and Complex Analysis, 1:58-73, 1994. MR 96b:47057
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- L. Rodman, I. M. Spitkovsky, and H. J. Woerdeman.
Factorization of almost periodic matrix functions of several variables and Toeplitz operators.
Operator Theory: Advances and Applications, 122 (H. Bart, I. Gohberg, A.C.M. Ran, eds.): 385-416, 2001.
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Additional Information
Leiba Rodman
Affiliation:
Department of Mathematics, The College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
Email:
lxrodm@math.wm.edu
Ilya M. Spitkovsky
Affiliation:
Department of Mathematics, The College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
Email:
ilya@math.wm.edu
Hugo J. Woerdeman
Affiliation:
Department of Mathematics, The College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
Email:
hugo@math.wm.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-01-06276-1
PII:
S 0002-9939(01)06276-1
Keywords:
Almost periodic functions,
Toeplitz operators,
Fredholmness
Received by editor(s):
October 28, 2000
Posted:
September 19, 2001
Additional Notes:
The research of all three authors was partially supported by NSF grant DMS-9988579.
Communicated by:
Joseph A. Ball
Article copyright:
© Copyright 2001 American Mathematical Society
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